Viscous Turbulent Flow Research Articles

A face-centred finite volume method for laminar and turbulent incompressible flows

This work develops, for the first time, a face-centred finite volume (FCFV) solver for the simulation of laminar and turbulent viscous incompressible flows. The formulation relies on the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the negative Spalart–Allmaras (SA) model and three novel convective stabilisations, inspired by Riemann solvers, are derived and compared numerically. The resulting method achieves first-order convergence of the velocity, the velocity-gradient tensor and the pressure. FCFV accurately predicts engineering quantities of interest, such as drag and lift, on unstructured meshes and, by avoiding gradient reconstruction, the method is less sensitive to mesh quality than other FV methods, even in the presence of highly distorted and stretched cells. A monolithic and a staggered solution strategies for the RANS-SA system are derived and compared numerically. Numerical benchmarks, involving laminar and turbulent, steady and transient cases are used to assess the performance, accuracy and robustness of the proposed FCFV method.

Исследование влияния химического состава воздушной среды на аэродинамику полета малых летательных аппаратов

The work is devoted to the study of the influence of an air environment with different chemical composition on the aerodynamics of small aircrafts of the airplane type used for reconnaissance purposes in case of fires. The thermodynamic properties of the combustion products formed during the combustion of rubber and foam rubber were calculated. The properties of the medium were taken into account in the mathematical modeling of the flight aerodynamics of an unmanned aerial vehicle. The mathematical model is based on solving conservation equations in a non-isothermal formulation for a turbulent viscous compressible flow using the k-ε turbulence model. The pressure and velocity fields of the environment were obtained during the flow around the wing, and the values of drag and lift forces were compared in the presence of combustion products in the air and without them. In particular, the numerical calculations were carried out in the presence of a vertical temperature gradient in the design area simulating the heating of air masses during fires with the study of the influence of these gradients on the aerodynamic characteristics of the wing. The calculations show that with an increase in the vertical temperature gradient by 60 K/m, the values of lift and drag decrease by 5 %.

Accuracy evaluation of modern effective codes by comparing calculated and experimental data on the example of problem about supersonic viscous turbulent gas flow around the tandem of back-forcing and forward-forcing steps

Дано описание различных программных кодов для расчета полей течения в окрестности сложных конфигураций вязким потоком турбулентного сжимаемого газа. Проведена серия тестовых расчетов для тандема трехмерных клиньев разрежения и сжатия. Целью расчетов является анализ точности разрешения отрывных зон с использованием классических и вновь создаваемых методов. Для достижения цели описаны физические особенности течения и выполнено сравнение результатов расчетов, полученных разными кодами в рамках тестового случая «тандем клиньев сжатия и разрежения».

Pulsating Flow of a Viscous Fluid over a Cavity Containing a Compressible Gas Bubble

A two-dimensional pulsating flow of a viscous fluid in a plane channel whose wall has rectangular microcavities partially or completely filled with a compressible gas is investigated. This problem formulation can clarify the friction reduction mechanism in a laminar sublayer of a turbulent viscous boundary layer flow over a textured stripped superhydrophobic surface containing periodically arranged rectangular micro-cavities filled with gas. It is assumed that the dimensions of the cavities are much smaller than the channel thickness. On the macroscale, the problem of one-dimensional unsteady viscous flow in a plane channel with no-slip conditions on the walls and a harmonic variation of the pressure difference is solved. The solution obtained in this way is used for formulating non-stationary in time and periodic in space boundary conditions for the flow on the scale of a chosen cavity (microscale), with the instantaneous volume of the gas bubble in the cavity depending on the instantaneous pressure over the cavity. The flow on the microscale near a cavity with a gas bubble occurs in the Stokes regime. The numerical solution is obtained using an original version of the boundary element method. A parametric numerical study of the flow field in a pulsating shear flow over a cavity with a compressible gas bubble is performed. The averaged parameters characterizing the effective ‘velocity slip’ of viscous fluid and the friction reduction in a pulsating flow over a stripped superhydrophobic surface are calculated.

The Gas-Dynamic Efficiency Increase of the K-300 Series Steam Turbine Control Compartment

The paper proposes ways to increase the efficiency of nozzle control for steam power turbines of the K-300 series, that, along with the K-200 series turbines, form the basis of thermal energy in Ukraine. The object of study is considered to be the control compartment (CC) of the high-pressure cylinder (HPC) of the K-325-23.5 steam turbine. In the paper, the calculation and design of the control compartment of the steam turbine was performed using the complex methodology developed in IPMach NAS of Ukraine, that includes methods of different levels of complexity, from one-dimensional to models for calculation of spatial viscous flows, as well as analytical methods for spatial geometries of flow parts description based on limited number of parameterized values. The complex design methodology is implemented in the IPMFlow software package, which is a development of the FlowER and FlowER–U software packages. A model of a viscous turbulent flow is based on the numerical integration of an averaged system of Navier-Stokes equations, for the closure of which the two-term Tamman equation of state is used. Turbulent phenomena were taken into account using a SST Menter two-parameter differential turbulence model. The research was conducted for six operation modes in the calculation area, which consisted of more than 3 million cells (elementary volumes), taking into account the interdiscand diaphragm leakage. According to the results of numerical studies of the original control compartment of the K-325-23.5 steam turbine, it is shown that the efficiency in the flow part is quite low in all operation modes, including the nominal one (100% power mode), due to large losses of kinetic energy in the equalization chamber, as well as inflated load on the first stage. On the basis of the performed analysis of gas-dynamic processes, the directions of a control compartment flow part modernization are formed and themodernization itself is executed. In the new flow part, compared to the original one, there is a favorable picture of the flow in all operation modes, which ensures its high gas-dynamic efficiency. Depending on the mode, the efficiency of the control compartment increased by 4.9–7.3%, and the capacity increased by 1–2 MW. In the nominal mode (100% mode) the efficiency of the new control compartment, taking into account the interdisc and overbandage leakage, is 91%.

Evaluation of modelling parameters for computing flow-induced noise in a small high-speed centrifugal compressor

Developments in computing infrastructure and methods over the last decade have enhanced the potential of numerical methods to reasonably predict the aerodynamic noise. The generation and propagation of the flow induced noise are aerodynamic phenomena. Although the fluid flow dynamics and the resultant acoustics are both governed by mass and momentum conservation equations, former is of convective and/or diffusive nature while the latter is propagative showing insignificant attenuation due to viscosity except for small viscothermal losses. Aeroacoustic modelling of systems with intricate geometries and complex flow is still not mature due to challenges in the accurate tractable representation of turbulent viscous flows. Therefore, state-of-the-art for computing flow-induced noise in small centrifugal compressors is reviewed and critical evaluation of various parameters in the numerical model is undertaken in this work. The impact of various turbulence formulations along with corresponding spatial and temporal resolutions on performance and acoustic predictions are quantified. The performance predictions are observed to be within 1.5% of the measured values irrespective of turbulence and timestep parameters. The noise generated by the impeller is observed to be reasonably correlated with the measurements and the absolute values of the sound pressure levels along with decay rates predicted by LES and SBES formulations are better than the similar predictions from DES and URANS formulations. The impact of timestep size is observed and is determinant of the frequency up to which spectra can be appropriately resolved. Furthermore, results emphasise the importance of high spatial resolution for scale resolving turbulence formulations to yield better results and the information can be used to select appropriate numerical configuration considering time and accuracy trade-offs.

Turbulent drag modification in open channel flow over an anisotropic porous wall

Direct numerical simulations are carried out for incompressible viscous turbulent flows over a porous wall with reduced spanwise permeability. This paper is intended to examine how the anisotropy of a porous wall affects the turbulence characteristics and modifies the skin-friction drag and to demonstrate numerically how sensitive the turbulent drag is to the porous layer thickness in channel flows. Simulations are carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The thickness of the porous layer ranges from 0.9 to 54 viscous units. For each fixed permeability, the drag is observed to decrease for flow over the porous layer with a smaller thickness hp, while a drag increase occurs for a larger hp. The division between two regimes (drag-reducing and drag-increasing) highlights a critical roughness height hc*, which depends linearly on the spanwise permeability Reynolds number as hc* ∼ Rekz. A larger value of hc* suggests an increasing degree of drag reduction can be achieved in a relative wider range of the porous layer thickness. For the porous medium configurations considered, the maximum drag reduction rate obtained is about 20.3% at hp+=9 (hc* = 18.3, Rekz = 0.18).

Effects of Blade Fillet Structures on Flow Field and Surface Heat Transfer in a Large Meridional Expansion Turbine

This paper is a continuation of the previous work, aiming to explore the influence of fillet configurations on flow and heat transfer in a large meridional expansion turbine. The endwall of large meridional expansion turbine stator has a large expansion angle, which leads to early separation of the endwall boundary layer, resulting in excessive aerodynamic loss and local thermal load. In order to improve the flow state and reduce the local high thermal load, five typical fillet distribution rules are designed. The three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solver for viscous turbulent flows was used to investigate the different fillet configurations of the second stage stator blades of a 1.5-stage turbine, and which fillet distribution is suitable for large meridional expansion turbines. The influence of fillet structures on the vortex system and loss characteristics was analyzed, and its impact on wall thermal load was studied in detail. The fillet structure mainly affects the formation of horseshoe vortexes at the leading edge of the blade so as to reduce the loss caused by horseshoe vortexes and passage vortexes. The fillet structure suitable for the large meridional expansion turbine was obtained through the research. Reasonable fillet structure distribution can not only improve the flow state but also reduce the high thermal load on the wall surface of the meridional expansion turbine. It has a positive engineering guiding value.

Liquid sloshing in a two-dimensional rectangular tank: A numerical investigation with a T-shaped baffle

In this study, the liquid sloshing in a closed, partially filled, T-shaped baffled and unbaffled two-dimensional rectangular tank was numerically investigated. The tank was rotated with two different rotation angles of 4° and 8°, and a fixed angular velocity of 3.3 rad/s, which was determined by taking the natural frequency of the tank into consideration, for the filling depths of 50% and 75%. The baffle heights as well as the rotation angles and filling depths were systematically varied and the effect of these parameters on the hydrodynamic loads on the tank wall and free surface elevations was examined. The calculations were carried out in two different ways, by means of laminar and turbulent viscous flow solvers, which use the finite differences and finite volume discretization techniques in conjunction with the “volume of fluid” technique, respectively. The general flow topology, free surface deformations, and vorticity distributions are provided and discussed in detail. It was found that the baffle was fully effective in pressure and wave damping when its height was greater than 80% of the liquid level. • Laminar and turbulent flow computations were performed for the simulation of liquid sloshing in a two-dimensional rectangular tank with a T-shaped baffle. • The effect of the baffle height, liquid depth and rotational angles on the pressure levels acting on the side wall were demonstrated. • The topological features of the flow, free surface deformations and vorticity distributions at constant sloshing phases were presented.

Aerodynamic Improvement of a Compact Centrifugal Compressor

For the example of the JetCat P-200RX turbojet engine, optimization of the diffuser and straightening unit of a compact centrifugal compressor is considered, on the basis of a mathematical model of viscous turbulent air flow. The goal of optimization is to increase the isentropic (adiabatic) efficiency of the compressor.

ESTIMATION OF THE STRESS-STRAIN STATE OF THE BLADE BASED ON INTERPROGRAM INTERACTION OF PROGRAM COMPLEXES

Basis of numerical simulation of turbulent viscous gas flow, using the Navier-Stokes equations averaged the Reynolds (RANS-model), a static analysis of the gas turbine compressor blade was performed. The simulation of flow parameters in three-dimensional formulation was carried out. For the solution of system of the equations the iterative differential scheme was built. The initial equations are integrated numerically by use of the iterative explicit and implicit differential scheme with a second order approximation. The differential two-parametrical SST Menter's model is used as a model of turbulence. As a result, distributed pressure and velocities in the blades channel were obtained and unfavorable flow zones were identified. At the second stage, was developed algorithm by which the interrelation of the gas-dynamic and mechanical calculation program was established. As a result, distributed pressure was applied to the finite-element model of the blade and a static analysis was performed. Static calculation makes it possible to calculate the stress-strain state of the construction.

Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

The direct numerical simulation (DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the turbulent drag reduction are investigated. The simulation is carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The depth of the porous layer ranges from 0.9 to 54 viscous units. The permeability in the spanwise direction is set to be lower than the other directions in the present simulation. The maximum drag reduction obtained is about 15.3% which occurs for a depth of 9 viscous units. The increasing of drag is addressed when the depth of the porous layer is more than 25 wall units. The thinner porous layer restricts the spanwise extension of the streamwise vortices which suppresses the bursting events near the wall. However, for the thicker porous layer, the wall-normal fluctuations are enhanced due to the weakening of the wall-blocking effect which can trigger strong turbulent structures near the wall.

Effect of Tip Clearance on Flow Field and Heat Transfer Characteristics in a Large Meridional Expansion Turbine

The large meridional expansion turbine stator leads to complex secondary flows and heat transfer characteristics in the blade endwall region, while the upstream tip clearance leakage flow of the rotor makes it more complex in flow and heat transfer. The influence of the upstream rotor tip clearance on the large meridian expansion stator is worth studying. The flow and heat transfer characteristics of the downstream large meridional expansion turbine stator were studied by comparing the tip leakage flow of 1.5-stage shrouded and unshrouded turbines using a three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solver for viscous turbulent flows. Validation studies were performed to investigate the aerodynamics and heat transfer prediction ability of the shear stress transport (SST) turbulence model. The influence of different tip clearances of the rotor including unshrouded blade heights of 0%, 1% and 5% and a 1% shrouded blade height were investigated through numerical simulation. The results showed that the upper passage vortex separation was more serious and the separation, and attachment point of horseshoe vortex in the pressure side were significantly more advanced than that of non-expansion turbines. The tip leakage vortex obviously increased the negative incidence angle at the downstream inlet. Furthermore, the strength of the high heat transfer zone on the suction surface of the downstream stator was significantly increased, while that of the shrouded rotor decreased.

Extension of a Non-Oscillatory Forward-in-Time Scheme to Detached Eddy Simulation of Stratified Turbulent Flows With Unstructured Meshes

A detached eddy simulation algorithm is developed based on the non-oscillatory forward-in-time (NFT) multidimensional positive definite advection transport algorithm (MPDATA) scheme for stratified turbulent flows with low or moderate Reynolds numbers on unstructured meshes. NFT MPDATA is extended to viscous turbulent flows for the first time. Viscous diffusion terms and an explicit sub-grid-scale model are included. The working viscosity of the modified Spalart-Allmaras one equation model is transported by an algorithm based on the NFT MPDATA template. The scheme is semi-implicit which solves the linear equation system once per time step. The advantage of the scheme is efficiency and second-order accuracy. Furthermore, an edge-based data structure is adopted such that our scheme is suitable for both structured and unstructured meshes. The linear equation system is solved by an efficient algebraic multigrid (AMG) method. The algorithm is validated using test cases with Reynolds numbers 200 and 5000 over a range of Froude numbers. The flow patterns and dynamic drag coefficients are analysed and compared to numerical and experimental data in literature.

Turbulent drag reduction by spanwise oscillations of a channel wall with porous layer

Direct numerical simulations (DNS) are carried out for the incompressible viscous turbulent flows over a spanwise-oscillating porous wall to investigate the effects of the oscillating porous wall on turbulence modifications as well as on turbulent drag reduction. The lattice Boltzmann method (LBM) based on D3Q19 model is applied to perform the numerical computation. Different Darcy numbers and porosities of porous medium are considered to pursue a significant drag reduction. An analytical solution to the Stokes second problem with two different kinds of fluid is derived, which predicts that the presence of porous layer will speed up the oscillation of the fluid when the porous medium is embedded in the Stokes layer. The current strategy suggests that comparing with the effects of the oscillating smooth wall, the joint effects of the porous wall and its spanwise oscillation may attain a larger drag reduction.

Homogenization of a Large Eddy Simulation Model for Turbulent Fluid Motion Near a Rough Wall

In this paper, we are interested in the numerical simulation of a turbulent viscous flow in the vicinity of a periodic rough wall. To this aim, we consider a large eddy simulation (LES) model, and perform its asymptotic analysis, letting the period $$\varepsilon $$ of the roughness tend to zero. Relying on an homogenization method closely related to the two-scale convergence method (Allaire in SIAM J Math Anal 23(6):1482–1518, 1992; Nguetseng in SIAM J Math Anal 20(3):608–623, 1989), we exhibit a critical scaling associated with parameter $$\lambda :=\lim _{\varepsilon \rightarrow 0}{a_\varepsilon }/{\varepsilon ^{5/3}}$$ , where $$a_\varepsilon $$ stands for the amplitude of the roughness. In the critical regime $$0<\lambda <\infty $$ , the roughness effect is described by an additional, nonlinear friction term, that depends locally on the solution to a nonlinear auxiliary problem of boundary layer type. In the particular case of riblets, which is of major practical interest, we show that the directional invariance of the geometry results in a simplified expression of this extra term, and we propose a numerical method to simulate the homogenized LES model, based on that observation. Finally, we study the influence of parameter $$\lambda $$ on the flow approximated by the homogenized model, using different commonly used riblet shapes. Our simulations demonstrate that the extra friction term can be handled numerically, and may have an important influence on the results of LES in presence of roughness.

Comparison between experimental and numerical results of a packed-bed thermal energy storage system in continuous operation

This paper reports the comparison between the results obtained by experimental tests made on a thermal energy storage (TES) system of sensible heat type under continuous operation with numerical simulations performed with a CFD model. TES system consists of a packed bed of spherical particles of alumina and air used as heat transfer fluid. The study concerns the time-dependent behaviour of the temperature field inside the bed, highlighting the thermocline evolution and its deterioration after repeated charge/discharge cycles due to the thermal hysteresis with a consequent progressive reduction of the recoverable energy. It is demonstrated that this effect is reduced by loosening the temperature constraints set at the end of each phase, increasing the amount of recovered energy and reducing the number of cycles needed to obtain the steady state. The CFD model was carried out considering a two-dimensional axisymmetric computational domain with the porous bed coupled to the wall. The governing equations are solved for incompressible viscous turbulent flow and fully developed forced convection based on the two-phase transient model equation to calculate both fluid and solid temperatures. Satisfactory agreement between detailed experimental and numerical results is reached when inlet air temperature follows that measured during experimental tests during both charge/discharge phases. CFD model used is reliable for predicting the whole temperature field of the TES during continuous operation.

INFLUENCE OF TURBULENCE MODEL ON EXACTNESS CALCULATION OF WING AERODYNAMICS IN SUBSONIC STREAM

The analysis of some modern methods which provide the numerical simulation of the subsonic turbulent viscous flow with the complicated geometrical configuration bodies according to the timeexactness criterion is conducted. The three-dimensional simulation of viscous incompressible flowing around of wing with the profile of NACA-23012 by the finite elements method using six turbulence models is executed. The models used are the model of Spalart-Allmaras, the standard k-e model, Menter model of Shear Stress Transport, the models of Large Eddy Simulation and Detached Eddy Simulation, the model of Scale Adaptive Simulation. Some of these turbulence models features, advantages and disadvantages are mentioned. In the issue of numerical research the diagrams of drag, lift and wing torque coefficients versus the angle of attack in the range of –8 ÷ 26 degrees at the value of Reynolds number 4.4·105 are got. The compared of the expected wing aerodynamic parameters to the results of Central Aero- and Hydrodynamic Institute (TsAGI) experiment is executed. The table of the calculating error values between the wing lift (numerical calculation) and similar data of aerodynamic experiment at the critical angle of attack is put. For the considered class of three-dimensional problems of flow with the complicated geometrical configuration objects by the viscous incompressible flow the models of turbulence which provide the minimum of the calculation time and the maximum of the got results exactness are recommended. Such advisable models are the model of Spalart-Allmaras and k-ω Menter model of Shear Stress Transport.

Numerical study of camber and stagger angle effects on the aerodynamic performance of tandem-blade cascades

Jet engine manufacturers and designers are seeking for lighter and smaller type of axial compressors. Improving the aerodynamic characteristics of blades is carried out by controlling the boundary layer. One way to control the boundary layer is using tandem blades. Tandem-blade cascades are capable of using highly loaded stages for axial compressors because they provide more works than single-blade cascades. In other words, tandem blades help to achieve a specified total pressure ratio with less number of stages. Therefore, one of the most important problems for researchers is to optimize the aerodynamic parameters of tandem blades. Changing the geometrical parameters of blades is a method to achieve this purpose.In this work, the stagger and camber angle of each blade are first changed while the other geometrical parameters such as overall camber, total stagger angle, the axial overlap, percent pitch and chord ratio are fixed. Secondly, the overall camber angle of tandem blade is changed by increasing the difference between the stagger angle of the first and second blade while the type of two airfoils, axial overlap and percent pitch, overall chord length and overall stagger angle are fixed.The aerodynamic performances of the generated tandem-blade cascades are obtained using two-dimensional numerical solution of flow. For this, a viscous turbulent flow solver is used for solving the Navier-Stokes equations. In these simulations, inlet Mach number is fixed to 0.6.

Separasi dan Reattachment Aliran di Belakang Gundukan (Bump) Setengah Lingkaran, Segitiga dan Persegi Panjang

&#x0D; Characteristic of viscous flow through a contour always become the interesting topic to be studied. This research studied characteristic of turbulent viscous flow through a flat plate mounted by bump. Target of this research is to know the flow characteristic through the semicircle, triangle and quadrangular bump, and also to get distribution coefficient of pressure (Cp), separation point, coefficient of pressure drag (CDp) and coefficient of total drag (CD). Beside that, in this research also conduct smoke visualization to know visualization of turbulent viscous flow through a flat plate mounted by bump. This experiment is conducted in subsonic wind tunnel. Form of the bump that is used are semicircle, triangle and quadrangular, and free stream velocity equal to 9.75 m/s and 15.5 m/s. Pressure coefficient got from static pressure measurement over flat plate and bump by using wall pressure tap. Coefficient of pressure drag (CDp) got from calculation based pressure. The measurement of velocity profile over flat plate and bump by using pitot tube. Measurement conducted at 6 point before side of upstream bump, 1 point at top bump and 13 point after side of downstream bump where distance between the points are 20 mm. While for the direction of vertical, the measurement taken at 80 point started from height 80 mm from surface until near the surface. Existence of bump on flat plate result the flow becomes separation so that generate the total drag force addition over flat plate. The highest total drag force occured on flat plate with triangle bump, then on flat plate with quadrangular bump and the smallest occur on flat plate with semicircle bump.